How do I make spikes show wherever you would see solidify lines with flipped normals?
This seems like a task for the compositor, but you explicitly stated that you don't want to render multiple times. That means only AOVs remain an option for compositing. After trying it I discarded the idea, because it will cause artifacts. Instead I found a solution using only the shader and some Custom Normals.
First you need to redo the spikes. You need a spike geometry with Custom Normals pointing along the spike direction. You can do that in Editmode of the spike by using Mesh &gt; Normals &gt; Point to Target or using Alt+L. Then you can use instancing to put the spikes at the vertices of your model. Then you need to disable ray visibility for any other ray than a camera ray in the object settings of your spikes.
After this setup you can make this shader:

The result looks like this:

You are also free to change your material in any way you want, which could have been difficult with the compositor approach.
Here is the Blend File: